JEE Main Mathematics Sets and Relations Online Test

JEE Main Mathematics Sets and Relations Online Test

Time limit: 0

Finish Quiz

0 of 20 questions completed

Questions:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Information

JEE Main Mathematics Sets and Relations Online Test. JEE Main Online Test for Mathematics Sets and Relations. JEE Main Full Online Quiz for Mathematics Sets and Relations. JEE Main Free Mock Test Paper 2017. JEE Main 2017 Free Online Practice Test, Take JEE Online Test for All Subjects. JEE Main Question and Answers for Mathematics Sets and Relations. In this test You may find JEE Main all subjects Questions with Answers. Check JEE Main Question and Answers in English. This mock Test is free for All Students. Mock Test Papers are very helpful for Exam Purpose, by using below Mock Test Paper you may Test your Study for Next Upcoming Exams. Now Scroll down below n Take JEE Main Mathematics Sets and Relations…

This paper has 20 questions.

Time allowed is 30 minutes.

The JEE Main Mathematics Sets and Relations is Very helpful for all students. Now Scroll down below n click on “Start Quiz” or “Start Test” and Test yourself.

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Results

0 of 20 questions answered correctly

Your time:

Time has elapsed

You have reached 0 of 0 points, (0)

Average score

Your score

Categories

Not categorized0%

maximum of 20 points

Pos.

Name

Entered on

Points

Result

Table is loading

No data available

Your result has been entered into leaderboard

Loading

Name:
E-Mail:

Captcha:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Answered

Review

Question 1 of 20

1. Question

Let n(a) = m and b = (n). Then, the total number of non-empty relations that can be defined from A to B is

2mn - 1

mn

nm - 1

mn - 1

Correct

Given , n(A) = m and n(B) = n

∴ Total number of relations from A to B = 2mn

∴ Total number of non-empty relations from A to B = 2mn –1

Incorrect

Given , n(A) = m and n(B) = n

∴ Total number of relations from A to B = 2mn

∴ Total number of non-empty relations from A to B = 2mn –1

Question 2 of 20

2. Question

If A and B are two sets then (A – B) ∪ (B – A) ∪ (A ∩ B) is equal to

A ∩ B

A

A ∪ B

B

Correct

From Venn-Euler’s diagram,

∴ (A – B) ∪ (B – A) ∪ (A ∩ B) = A ∪ B.

Incorrect

From Venn-Euler’s diagram,

∴ (A – B) ∪ (B – A) ∪ (A ∩ B) = A ∪ B.

Question 3 of 20

3. Question

R is a relation from (11, 12, 13) to (8, 10, 12) defined by y = x – 3 The relation R-1 is

{(11, 8), (13, 10)}

{(8, 11), (10, 13)}

{(8, 11), (9, 12), (10, 13)}

None of these

Correct

Let A = {11, 12, 13}, B = {8, 10, 12}

∴ R = {(11, 8), (13, 10)}

R-1 = {(8, 11), (10, 13)}

Incorrect

Let A = {11, 12, 13}, B = {8, 10, 12}

∴ R = {(11, 8), (13, 10)}

R-1 = {(8, 11), (10, 13)}

Question 4 of 20

4. Question

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is

29

6

8

None of these

Correct

n(A × A) = n(A). n(A) = 32 = 9

So, the total number of subsets of A × A is 29 and a subset of A × A is a relation over the set A.

Incorrect

n(A × A) = n(A). n(A) = 32 = 9

So, the total number of subsets of A × A is 29 and a subset of A × A is a relation over the set A.

Question 5 of 20

5. Question

Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}. The relation R-1 or is given by

{(1, 1), (4, 4), (7, 4), (4, 7), (7, 7)}

{(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}

{(1, 5), (1, 6), (3, 6)}

None of the above

Correct

Given, R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}

∴ R-1 = {(5, 4), (4, 1), (6, 4), (6, 7), (7, 3)}

⇒ R-1 or = {(4, 4), (1, 1), (4, 7), (7, 4), (7, 7), (3, 3)}

Incorrect

Given, R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}

∴ R-1 = {(5, 4), (4, 1), (6, 4), (6, 7), (7, 3)}

⇒ R-1 or = {(4, 4), (1, 1), (4, 7), (7, 4), (7, 7), (3, 3)}

Question 6 of 20

6. Question

The solution set of the equation x3 – 3x + 2 = 0 in roster from is

{1, 2}

{1, 2, 3}

{1, -2}

{-1, 2}

Correct

On solving x3 – 3x + 2 = 0

we get x = 1 & -2

∴ Solution set is {1, -2}

Incorrect

On solving x3 – 3x + 2 = 0

we get x = 1 & -2

∴ Solution set is {1, -2}

Question 7 of 20

7. Question

The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by

9. Question

Let R be the relation from A = {2, 3, 4, 5} to B = {3, 6, 7, 10} defined by ‘x devides y’, then R-1 is equal to

{(6, 2), (3, 3)}

{(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}

{(6, 2), (10, 2), (3, 3), (6, 3)}

None of the above

Correct

Given, A = {2, 3, 4, 5} and B = {3, 6, 7, 10}

∴ R = {(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}

⇒ R-1 = {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}

Incorrect

Given, A = {2, 3, 4, 5} and B = {3, 6, 7, 10}

∴ R = {(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}

⇒ R-1 = {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}

Question 10 of 20

10. Question

If R is an equivalence relation on a set A, then R–1 is NOT

Reflexive

Symmetric

Transitive

None of these

Correct

Incorrect

Question 11 of 20

11. Question

If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR

is from C to A

is from A to C

does not exist

none of these

Correct

Give, R ⊆ A × B and S ⊆ B × B, we have

So r ⊆ A × C

∴ SoR is a relation from A to C.

Incorrect

Give, R ⊆ A × B and S ⊆ B × B, we have

So r ⊆ A × C

∴ SoR is a relation from A to C.

Question 12 of 20

12. Question

The number of elements in the power set of {a, b, c}

3

7

8

6

Correct

Number of subsets of {a, b, c} = 23 = 8 ∴ number of elements in the power set = 8

Incorrect

Number of subsets of {a, b, c} = 23 = 8 ∴ number of elements in the power set = 8

Question 13 of 20

13. Question

The set {0, 2, 6, 12, 20} in the set-builder form is

{x : x = n2 - 3n + 2, where 'n' is a natural number & 1 ≤ n ≤ 6}

{x : x = n2 - 3n + 2, where n is a natural number & 1 ≮ n ≤ 5}

{x : x = n2 - 3n + 4, where 'n' is a natural number & 1 ≤ n ≤ 5}

{x : x = n2 + 5n - 6, where n is natural number & 1 ≤ n ≤ 5}

Correct

We see that each number in the given set follow the relation x = n2 – 3n + 2 as for

n = 1, x = 1 – 3 + 2 = 0

n = 2, x = 4 – 6 + 2 = 0

n = 3, x = 9 – 9 + 2 = 2

n = 4, x = 16 – 12 + 2 = 6

n = 5, x = 25 – 15 + 2 = 12

n = 6, x = 36 – 18 + 2 = 20

Incorrect

We see that each number in the given set follow the relation x = n2 – 3n + 2 as for

n = 1, x = 1 – 3 + 2 = 0

n = 2, x = 4 – 6 + 2 = 0

n = 3, x = 9 – 9 + 2 = 2

n = 4, x = 16 – 12 + 2 = 6

n = 5, x = 25 – 15 + 2 = 12

n = 6, x = 36 – 18 + 2 = 20

Question 14 of 20

14. Question

The set equivalent to the set {1, 2, 3, 4, 5, 6} is

{3, 4, 1, 5, 2, 6}

{1, 2, 4, 5, 6}

{x : x = n, where n is natural number and n < 7}

{6, 5, 4, 3, 2}

Correct

A set does not change if the order of the elements is changed.

Incorrect

A set does not change if the order of the elements is changed.

Question 15 of 20

15. Question

Let R = {(a, a)} be a relation on a set A, Then R is

Antisymmetric

Transitive

Neither symmetric nor anti-symmetric

Symmetric

Correct

Incorrect

Question 16 of 20

16. Question

The number of proper subsets of the set {1, 2, 3} is

6

8

7

5

Correct

Number of proper subsets = 23 – 2 = 6

Incorrect

Number of proper subsets = 23 – 2 = 6

Question 17 of 20

17. Question

If A and B are two given sets, then A ∪ (A ∩ B) is equal to

B

A<sup>C</sup>

B<sup>C</sup>

A

Correct

A ∩ B ∩ A. Hence A ∪ (A ∩ B) = A

Incorrect

A ∩ B ∩ A. Hence A ∪ (A ∩ B) = A

Question 18 of 20

18. Question

If A = {x : x is an integer, x2< 1}, then the elements of ‘A’ are

{0, 1}

{–1, 0}

{–1, 0, 1}

None of these

Correct

If x2< 1 ⇒ –1 < x < 1 & x is an integer ∴ x ∈ {–1, 0, 1}

Incorrect

If x2< 1 ⇒ –1 < x < 1 & x is an integer ∴ x ∈ {–1, 0, 1}

Question 19 of 20

19. Question

In a town of 10, 000 families it was found that 40% family buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families by A and B, 3% buy B and C and 4% buy A and C. If 2%families buy all the three newspapers, then number of families which buy A only is